Any way to "thicken" my model without scaling it?
Well, it turns out I should have kept trying for another half hour before posting.
For anyone else with this problem, select all in edit mode, hit Alt+S to scale along normals, and then, while scaling, hold Alt or S to use something called Even Thickness to keep it from &quot;bubbling&quot; out.
I'll wait a while to mark this as my answer, in case someone else has another option that works better